Maximum likelihood estimation in panels with incidental trends

It is shown that the maximum likelihood estimator of a local to unity param eter can be consistently estimated with panel data when the cross-section o bservations are independent. Consistency applies when there are no determin istic trends or when there is a homogeneous deterministic trend in the pane l model. When there are heterogeneous deterministic trends the panel MLE of the local to unity parameter is inconsistent. This outcome provides a new instance of inconsistent ML estimation in dynamic panels, and, unlike earli er results of this type, applies when both T --> infinity and N --> infinit y.